Messi won the Champions League four times with Barca between 2006 and 2015 but has seen arch-rivals Madrid claim it in four of the last five seasons.
Antoine Griezmann is believed to be on the verge of announcing his intention to stay at Atletico Madrid this summer, and has called a press conference in order to confirm that he will renew his contract at the Wanda Metropolitano - rejecting the offer from Barcelona in the process.
Barca's pursuit has angered Atletico, who in December reported them to Federation Internationale de Football Association for making an alleged illegal approach and followed up with a statement in May that said "enough is enough".
"It's good that you're taking an interest", Griezmann told reporters.
"I don't know what happened against the United States of America, we prepared well".
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France coach Didier Deschamps prohibits players from undergoing negotiations during tournaments, pushing Griezmann towards making a decision.
According to French outlet Canal+, Griezmann has chose to stay with Atletico and sign a new deal which would make him the highest paid player in their history.
Argentina superstar Lionel Messi has admitted that Frenchman Antoine Griezmann will be of great advantage for Barcelona if the club signs him this summer.
After facing the USA on Saturday in Lyon, France are due to fly to their training base near Moscow on Sunday.
The media gathered at France's World Cup base in Russian Federation to attend a press conference, at which Griezmann would be speaking.